- 2.6.1: In 1 and 2, use Euler's method to obtain a four-decimal approximati...
- 2.6.2: In 1 and 2, use Euler's method to obtain a four-decimal approximati...
- 2.6.3: In 3 and 4, use Euler's method to obtain a four-decimal approximati...
- 2.6.4: In 3 and 4, use Euler's method to obtain a four-decimal approximati...
- 2.6.5: In 5-10, use a numerical solver and Euler's method to obtain a four...
- 2.6.6: In 5-10, use a numerical solver and Euler's method to obtain a four...
- 2.6.7: In 5-10, use a numerical solver and Euler's method to obtain a four...
- 2.6.8: In 5-10, use a numerical solver and Euler's method to obtain a four...
- 2.6.9: In 5-10, use a numerical solver and Euler's method to obtain a four...
- 2.6.10: In 5-10, use a numerical solver and Euler's method to obtain a four...
Solutions for Chapter 2.6: A Numerical Method
Full solutions for Advanced Engineering Mathematics | 5th Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
See Arithmetic mean.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
A probability distribution for a discrete random variable
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
The variance of an error term or component in a model.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
A series of tests in which changes are made to the system under study
Fraction defective control chart
See P chart
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .